On solving a non-convex quadratic programming problem involving resistance distances in graphs
Annals of Operations Research
Quadratic programming problems involving distance matrix (D) that arises in trees are considered in the literature by Dankelmann (Discrete Math 312:12–20, 2012), Bapat and Neogy (Ann Oper Res 243:365–373, 2016). In this paper, we consider the question of solving the quadratic programming problem of finding maximum of xTRx subject to x being a nonnegative vector with sum 1 and show that for the class of simple graphs with resistance distance matrix (R) which are not necessarily a tree, this problem can be reformulated as a strictly convex quadratic programming problem. An application to symmetric bimatrix game is also presented.
Dubey, Dipti and Neogy, S. K., "On solving a non-convex quadratic programming problem involving resistance distances in graphs" (2020). ISI Best Publications. 87.